Multicritical Fermi Surface Topological Transitions.

A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are enhanced through density of states peaks. A well-known example occurs at van Hove singularities where the Fermi surface undergoes a topological transition. Here we show that higher order singularities, where multiple disconnected leaves of Fermi surface touch all at once, naturally occur at points of high symmetry in the Brillouin zone. Such multicritical singularities can lead to stronger divergences in the density of states than canonical van Hove singularities, and critically boost the formation of complex quantum phases via interactions. As a concrete example of the power of these Fermi surface topological transitions, we demonstrate how they can be used in the analysis of experimental data on Sr_{3}Ru_{2}O_{7}. Understanding the related mechanisms opens up new avenues in material design of complex quantum phases.

Effects of Lifshitz Transitions in Ferromagnetic Superconductors: The Case of URhGe.

In ferromagnetic superconductors, like URhGe, superconductivity coexists with magnetism near zero field, but then reappears in a finite field range, where the system also displays mass enhancement in the normal state. We present the theoretical understanding of this nonmonotonic behavior. We explore the multiband nature of URhGe and associate reentrant superconductivity and mass enhancement with the topological transition (Lifshitz) in one of the bands in a finite magnetic field. We find excellent agreement between our theory and a number of experimental results for URhGe, such as weakly first-order reentrant transition, the dependence of superconducting T_{c} on a magnetic field, and the field dependence of the effective mass, the specific heat, and the resistivity in the normal state. Our theory can be applied to other ferromagnetic multiband superconductors.

Magnetic fluctuations and specific heat in Na(x)CoO2 near a Lifshitz transition.

We analyze the temperature and doping dependence of the specific heat C(T) in Na(x)CoO(2). This material was conjectured to undergo a Lifshitz-type topological transition at x=x(c)=0.62, in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large k(F). The data show that near x=x(c), the temperature dependence of C(T)/T at low T gets stronger as x approaches x(c) from below and then reverses the trend and changes sign at x≥x(c). We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near x(c) at momenta around k(F), and their dynamics changes between x≤x(c) and x>x(c), when the new pocket forms. We demonstrate that this explains the temperature dependence of C(T)/T. We show that at larger x (x>0.65) the system enters a magnetic quantum critical regime where C(T)/T roughly scales as logT. This behavior extends to progressively lower T as x increases towards a magnetic instability at x≈0.75.

Non-Landau damping of magnetic excitations in systems with localized and itinerant electrons.

We discuss the form of the damping of magnetic excitations in a metal near a ferromagnetic instability. The paramagnon theory predicts that the damping term should have the form γ(q,Ω)∝Ω/Γ(q), with Γ(q)∝q (the Landau damping). However, the experiments on uranium metallic compounds UGe2 and UCoGe showed that Γ(q) is essentially independent of q. A nonzero γ(q=0,Ω) is impossible in systems with one type of carrier (either localized or itinerant) because it would violate the spin conservation. It has been conjectured recently that a near-constant Γ(q) in UGe2 and UCoGe may be due to the presence of both localized and itinerant electrons in these materials, with ferromagnetism involving predominantly localized spins. We present the microscopic analysis of the damping of near-critical localized excitations due to interaction with itinerant carriers. We show explicitly how the presence of two types of electrons breaks the cancellation between the contributions to Γ(0) from the self-energy and vertex correction insertions into the spin polarization bubble. We compare our theory with the available experimental data.

First-order versus unconventional phase transitions in three-dimensional dimer models.

We study the phase transition between the Coulomb liquid and the columnar crystal in the 3D classical dimer model, which was found to be continuous in the O(3) universality class. In addition to nearest-neighbor interactions which favor parallel dimers, further neighbor interactions are allowed in such a manner that the cubic symmetry of the original system remains intact. We show that the transition in the presence of weak additional, symmetry preserving interactions is first order. However, the universality class of the transition remains continuous when the additional interactions are weakly repulsive. In this way, we verify the existence of a multicritical point near the unperturbed transition, and we identify a critical line of unconventional transitions between the Coulomb liquid phase and the sixfold columnar phase.

Multiferroicity induced by dislocated spin-density waves.

We uncover a new pathway towards multiferroicity, showing how magnetism can drive ferroelectricity without relying on inversion symmetry breaking of the magnetic ordering. Our free-energy analysis demonstrates that any commensurate spin-density-wave ordering with a phase dislocation, even if it is collinear, gives rise to an electric polarization. Because of the dislocation, the electronic and magnetic inversion centers do not coincide, which turns out to be a sufficient condition for multiferroic coupling. The novel mechanism explains the formation of multiferroic phases at the magnetic commensurability transitions, such as the ones observed in YMn(2)O(5) and related compounds. We predict that in these multiferroics an oscillating electrical polarization is concomitant with the uniform polarization. On the basis of our theory, we put forward new types of magnetic materials that are potentially ferroelectric.

Correlated fermions on a checkerboard lattice.

A model of strongly correlated spinless fermions on a checkerboard lattice is mapped onto a quantum fully packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states. Furthermore, we analyze excitations at the Rokhsar-Kivelson point of this model using the relation to the height model and the single-mode approximation.